Factor the expression by grouping. First, the expression needs to be rewritten as $x^{2}+ax+bx-20$. To find $a$ and $b$, set up a system to be solved.
$$a+b=-1$$ $$ab=1\left(-20\right)=-20$$
Since $ab$ is negative, $a$ and $b$ have the opposite signs. Since $a+b$ is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product $-20$.
$$1,-20$$ $$2,-10$$ $$4,-5$$
Calculate the sum for each pair.
$$1-20=-19$$ $$2-10=-8$$ $$4-5=-1$$
The solution is the pair that gives sum $-1$.
$$a=-5$$ $$b=4$$
Rewrite $x^{2}-x-20$ as $\left(x^{2}-5x\right)+\left(4x-20\right)$.
$$\left(x^{2}-5x\right)+\left(4x-20\right)$$
Factor out $x$ in the first and $4$ in the second group.
$$x\left(x-5\right)+4\left(x-5\right)$$
Factor out common term $x-5$ by using distributive property.
$$\left(x-5\right)\left(x+4\right)$$
Steps Using the Quadratic Formula
Quadratic polynomial can be factored using the transformation $ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right)$, where $x_{1}$ and $x_{2}$ are the solutions of the quadratic equation $ax^{2}+bx+c=0$.
$$x^{2}-x-20=0$$
All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$. The quadratic formula gives two solutions, one when $±$ is addition and one when it is subtraction.
